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Purple furry monter happy to have a tongue
Time to get purple furry monster's tongue into the mouth. I cut the tongue in a heart shape from red fleece. (Just like cutting a heart from paper folded in half!) I hot glue the tongue in after I set it in a couple different positions to get it "just right". I've found it's good to walk at least 6-10 feet away to get a good look at how it looks from farther away.
This puppet doesn't have teeth, but I think this a great place to talk about how I do teeth. I carve them with an embroidery scissor from latex makeup sponges. For the particular teeth shown in the pictures, I also "aged" and added plaque to the teeth with 3 different shades of brown markers.
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Grungy monster teeth built from makeup sponges
 
To build a puppet, I first have to get the character in my head down onto the paper. Sometimes this comes easily, other times there's kicking and screaming. Draw, draw, draw. Lots of paper might end up in the recycle bin, but better than fur and feathers.
I like to use Prismacolor markers and a Sharpie pen on plain printer paper. Once I get a black and white sketch that I am happy with, I scan it, then print it out. That way, if I mess up in the coloring process- I just print out another page and color again.